Today was the suck. We will not speak it.
Re: Possessiveness
My Shepard isn't possessive. She loves Kaidan, but if it wasn't working out, well... she'd prefer to see him happy than force him to stay with her. Not that he would be likely to, but the only time she would be pissed with him was if he were cheating on her - and that more for the not upfront bit than he wasn't into her bit.
I can see Kaidan getting possessive after the Normandy was destroyed (and you could argue that his anger on Horizon was partly because Shepard chose Cerberus over him). I can see him being kinda possessive if he gets to the pre-Ilos night. But I think he'd be somewhat communicative about it. He would probably be hurt if Shepard decided that wasn't what she wanted, but I don't think he'd fight with her overly much if she wanted to leave.
I don't think he was possessive during the courting stage, though - and I do think that his anger during the Liara confrontation was less possessive (maybe a little), but more he thought Shepard was pulling a Captain Kirk on him and he didn't want to be jerked around.
Re: Dining
All-You-Can-Eat or Buffet type deals would probably be the most convenient, depending on whether it was good food or not. More... uh... traditional? type dining with the waiter types and all that, Kaidan would probably go for but there would be much snacking either before or after to keep up.
And if my Shepard were involved, she would probably be decked out in full armor, so the whole "romantic atmosphere" might be compromised.
Re: Liara
Again, I think Kaidan and Liara could have had a brief fling after Shepard's funeral, because funerals can do that to people, Liara has been in Shepard's head, and Kaidan has memories of Shepard that Liara doesn't.
Re: Grieving
Although I think Kaidan may have been on the cusp of moving on, I don't think grief studies take into account zombie!cyborg!girlfriends working for the enemy.